Forces free energy, Gibbs

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

A solution is a single-phase mixture of more than one compound, and the driving force for its spontaneous formation from the pure compounds at constant T and p is the negative Gibbs free energy change of the mixing process, —AG, as... 

C = U — Ts -j-pv ( force function for constant pressure ), j X = U + pv ( heat function for constant pressure ) are constantly used, and they are frequently referred to as the psi, zeta, and chi functions of Gibbs. The zeta function is identical with our free energy, whilst the x function is the heat function at constant pressure of 25. 

The electromotive force of a cell can be related to the Gibbs free energy change for the cell reaction by combining equations (9.5), (9.90), and (3.96). We recall that... 

Redox reactions that have a positive Gibbs free energy of reaction are not spontaneous, but an electric current can be used to make them take place. For example, there is no common spontaneous chemical reaction in which fluorine is a product, and so the element cannot be isolated by any common chemical reaction. It was not until 1886 that the French chemist Henri Moissan found a way to force the... 

Frasch process A process for mining sulfur that uses superheated water to melt the sulfur and compressed air to force it to the surface, free energy See Gibbs free energy. free expansion Expansion against zero opposing pressure. 

The quantity of primary interest in our thermodynamic construction is the partial molar Gibbs free energy or chemical potential of the solute in solution. This chemical potential reflects the conformational degrees of freedom of the solute and the solution conditions (temperature, pressure, and solvent composition) and provides the driving force for solute conformational transitions in solution. For a simple solute with no internal structure (i.e., no intramolecular degrees of freedom), this chemical potential can be expressed as... 

The structure of hydrogels that do not contain ionic moieties can be analyzed by the Flory Rehner theory (Flory and Rehner 1943a). This combination of thermodynamic and elasticity theories states that a cross-linked polymer gel which is immersed in a fluid and allowed to reach equilibrium with its surroundings is subject only to two opposing forces, the thermodynamic force of mixing and the retractive force of the polymer chains. At equilibrium, these two forces are equal. Equation (1) describes the physical situation in terms of the Gibbs free energy. 

Once an exothermic decomposition is initiated, usually by application of heat to raise the temperature, the energy that is released may maintain the higher temperature and thus cause the reaction to continue until all material is converted or until the reaction is stopped by forced cooling. The change in the Gibbs free energy during such a process (at constant temperature and pressure) is ... 

Electrode reactions are inner-sphere reactions because they involve adsorption on electrode surfaces. The electrode can act as an electron source (cathode) or an electron sink (anode). A complete electrochemical cell consists of two electrode reactions. Reactants are oxidized at the anode and reduced at the cathode. Each individual reaction is called a half cell reaction. The driving force for electron transfer across an electrochemical cell is the Gibbs free energy difference between the two half cell reactions. The Gibbs free energy difference is defined below in terms of electrode potential,... 

Molecules in the surface or interfacial region are subject to attractive forces from adjacent molecules, which result in an attraction into the bulk phase. The attraction tends to reduce the number of molecules in the surface region (increase in inter-molecular distance). Hence work must be done to bring molecules from the interior to the interface. The minimum work required to create a differential increment in surface dA is ydA, where A is the interfacial area and y is the surface tension or interfacial tension. One also refers to y as the interfacial Gibbs free energy for the condition of constant temperature, T, pression, P, and composition (n = number of moles)... 

For the industrially important class of mixed solvent, electrolyte systems, the Pitzer equation is not useful because its parameters are unknown functions of solvent composition. A local composition model is developed for these systems which assumes that the excess Gibbs free energy is the sum of two contributions, one resulting from long-range forces between ions and the other from short-range forces between all species. 

The most important property of a liquid-gas interface is its surface energy. Surface tension arises at the boundary because of the grossly unequal attractive forces of the liquid subphase for molecules at its surface relative to their attraction by the molecules of the gas phase. These forces tend to pull the surface molecules into the interior of the liquid phase and, as a consequence, cause liquids to minimize their surface area. If equilibrium thermodynamics apply, the surface tension 7 is the partial derivative of the Helmholtz free energy of the system with respect to the area of the interface—when all other conditions are held constant. For a phase surface, the corresponding relation of 7 to Gibbs free energy G and surface area A is shown in eq. [ 1 ]. 

At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs free energy. Some reactions are spontaneous because they give off energy in the form of heat (AH<0). Other reactions are spontaneous because they lead to an increase in the disorder of the system (AS>0). Calculations of AH and AS can be used to probe the driving force behind a particular reaction. 

Because, as we have already seen, the standard potential of hydrogen is zero, the electromotive force of the galvanic cell (eq. 8.161) directly gives the value of the standard potential for the Zn,Zn redox couple. Table 8.14 lists the standard potentials for various aqueous ions. The listed values are arranged in decreasing order and are consistent with the standard partial molal Gibbs free energies of table 8.13. 

Chemical work and chemical energy are defined in an analogous way. The intensity factor here is the chemical potential of a molecule or combination of molecules. This is stated as free enthalpy G (also known as Gibbs free energy ). When molecules spontaneously react with one another, the result is products at lower potential. The difference in the chemical potentials of the educts and products (the change in free enthalpy, AC) is a measure of the driving force of the reaction. The capacity factor in chemical work is... 

Because most biological systems are operative under conditions of constant pressure, changes in G are quite useful to describe driving forces for a wide variety of processes. The sign of the change in Gibbs free energy,... 

In order for mixing and solution to occur, it is essential that the change in free energy, AG, which is the driving force in the solution process, decrease to below zero. A/f and AG are equal to the change in enthalpy and change in entropy, and for constant temperature the relationship is the classical Gibbs equation ... 

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